For 2016). When steel fibre and barFor 2016). When steel fibre and bar

For the analysis of serviceability limit
state, models based on stress-transfer (also called force transfer, or partial
interaction) approach appears to be a reasonable alternative to commonly used
code techniques, as it realistically predicts the cracking behaviour of reinforced
concrete, bond-slip mechanics and the effect of tension stiffening (Jakubovskis et
al. 2013, Sokolov et al. 2016).

When steel fibre and bar reinforcement are
combined, the post cracking tensile capacity of the SFRC should be taken into
account when calculating crack widths and spacing for the elements with bar
reinforcement. In traditionally reinforced concrete members the crack width depends
on the distance between cracks, i.e. crack spacing, and the distance between
cracks is determined by the bond length of the reinforcing bars. At a crack the
tensile force in the plain concrete is zero with all the tensile force being
carried by the steel bar reinforcement. Further from the crack the reinforcing
bars bonded into the concrete matrix transfer tensile force into the concrete,
with all the force being transferred into the concrete at a distance equal to
the reinforcing bars development length. This distance in this research will be
called as stress-transfer length. This means that the minimum spacing between
cracks is one development length and the maximum spacing is two development
lengths. The maximum crack width will therefore result when the cracks are
spaced at the maximum spacing of two development lengths.

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The effect of steel fibres is to increase
the tensile force in the concrete at a crack from zero to the tensile capacity
of the cracked SFRC. The result of this is that the tensile force in the
conventional reinforcement at the crack is reduced and, therefore, the development
length of the steel is reduced. The same holds for the strain in the steel.
Reducing the development length and the strain of the reinforcement reduces the
maximum distance between cracks and, thus, results in more cracks but with a
smaller width.